Finite Group Databasebeta

← #20251650

Subgroups — #20251650

Order 6016.

396 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 125 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689064C212yesmaximal, complemented
2#15689056C212yesmaximal, complemented
3#15689053C212yesmaximal, complemented
4#15689046C212yesmaximal
5#15689043C212yesmaximal, complemented
6#15689035C211yesmaximal, characteristic
7#15688984C211yesmaximal, characteristic
8#15688981C212yesmaximal
9C47×#399C211yesmaximal, characteristic
10C22×Dic94C2211yescharacteristic
11C23×Dic47C2211yescharacteristic
12C2×C4⋊Dic47C2212yes—
13C2×Dic47⋊C4C2212yes—
14C2×Dic47⋊C4C2212yes—
15C2×Dic47⋊C4C2212yes—
16C2×Dic47⋊C4C2212yes—
17C2×C22⋊Dic47C2212yes—
18C2×C22⋊Dic47C2211yescharacteristic
19C47⋊#95C2212yes—
20C47⋊#95C2212yes—
21C47⋊#95C2212yes—
22C47⋊#95C2212yes—
23C47⋊#95C2211yescharacteristic
24C47⋊#95C2212yes—
25C47⋊#95C2212yes—
26C2×C4⋊C4×C47C2212yes—
27C2×C4⋊C4×C47C2211yescharacteristic
28C2×C22⋊C4×C47C2212yes—
29C2×C22⋊C4×C47C2211yescharacteristic
30#95×C47C2211yescharacteristic
31C24×C47C2311yescharacteristic
32C22×C4×C47C2311yescharacteristic
33C22×C4×C47C2312yes—
34C22×C4×C47C2311yescharacteristic
35C22×C4×C47C2312yes—
36C22×Dic47—41no—
37C22×Dic47—41no—
38C22×Dic47Q814yescomplemented
39C22×Dic47C2312yes—
40C22×Dic47C2312yes—
41C22×Dic47C2312yes—
42C22×Dic47C2312yes—
43C2×Dic94—41no—
44C2×Dic94—42no—
45C4⋊C4×C47—41no—
46C4⋊C4×C47—42no—
47C22⋊C4×C47—42no—
48C22⋊C4×C47—41no—
49C22⋊Dic47—41no—
50C22⋊Dic47—42no—
51C4⋊Dic47—42no—
52Dic47⋊C4—42no—
53Dic47⋊C4—42no—
54Dic47⋊C4—42no—
55Dic47⋊C4—42no—
56C23×C47—22no—
57C23×C47—21no—
58C23×C47—21no—
59C23×C47—22no—
60C23×C47C2×Q812yes—
61C23×C47C2411yescharacteristic
62C2×C4×C47—22no—
63C2×C4×C47—22no—
64C2×C4×C47—22no—
65C2×C4×C47—22no—
66C2×C4×C47—22no—
67C2×C4×C47—21no—
68C2×C4×C47—21no—
69C2×C4×C47—22no—
70C2×C4×C47—22no—
71C2×C4×C47—22no—
72C2×Dic47—22no—
73C2×Dic47—22no—
74C2×Dic47—22no—
75C2×Dic47—22no—
76C2×Dic47—22no—
77C2×Dic47—22no—
78C2×Dic47—22no—
79C2×Dic47—22no—
80C2×Dic47—22no—
81C2×Dic47—22no—
82C2×Dic47—22no—
83C2×Dic47—44no—
84C2×Dic47C2×Q814yes—
85Dic94—44no—
86C22×C47—22no—
87C22×C47—24no—
88C22×C47—41no—
89C22×C47—42no—
90C22×C47—41no—
91C22×C47C22×Q811yescharacteristic
92C22×C47H(5,𝔽2)11yescharacteristic
93C22×C47H(5,𝔽2)12yes—
94C22×C47H(5,𝔽2)11yescharacteristic
95C22×C472−1+412yes—
96C4×C47—41no—
97C4×C47—42no—
98C4×C47—42no—
99C4×C47—41no—
100Dic47—24no—
101Dic47—42no—
102Dic47—42no—
103Dic47—42no—
104#2841—471nomaximal, Sylow
105C2×C47—42no—
106C2×C47#54311yescharacteristic
107C2×C47#54412yes—
108C2×C47#56011yescharacteristic
109C2×C47#56212yes—
110C2×C47#56311yescharacteristic
111#400—472no—
112#399D4711yescharacteristic
113#398—472no—
114#398—472no—
115#396—472no—
116#395—472no—
117#393—471no—
118#381—471no—
119#380—472no—
120C47#284111yescharacteristic, complemented, Sylow
121C22×Q8—471no—
122C23×C4—471no—
123C2×C4⋊C4—472no—
124C2×C4⋊C4—472no—
125C2×C4⋊C4—472no—
126C2×C4⋊C4—472no—
127C2×C4⋊C4—472no—
128C2×C4⋊C4C2×D4712yes—
129C2×C4⋊C4C2×D4711yescharacteristic
130C2×C22⋊C4—472no—
131C2×C22⋊C4—471no—
132C2×C22⋊C4C2×D4712yes—
133C2×C22⋊C4C2×D4711yescharacteristic
134#95—472no—
135#95—472no—
136#95—472no—
137#95—472no—
138#95—471no—
139#95—472no—
140#95—472no—
141#95C2×D4711yescharacteristic
142C24C22×D4711yescharacteristic
143C2×Q8—1881no—
144C2×Q8—1882no—
145C22×C4—472no—
146C22×C4—474no—
147C22×C4—472no—
148C22×C4—472no—
149C22×C4—472no—
150C22×C4—1881no—
151C22×C4—1881no—
152C22×C4C22×D4711yescharacteristic
153C22×C4C22×D4711yescharacteristic
154C22×C4C22×D4712yes—
155C22×C4C22×D4712yes—
156C4⋊C4—41no—
157C4⋊C4—42no—
158C4⋊C4—1882no—
159C4⋊C4—1882no—
160C4⋊C4—1882no—
161C4⋊C4—1882no—
162C4⋊C4—1882no—
163C22⋊C4—42no—
164C22⋊C4—41no—
165C22⋊C4—1882no—
166C22⋊C4—1881no—
167C23—22no—
168C23—21no—
169C23—21no—
170C23—22no—
171C23Q8×D4712yes—
172C23C23×D4711yescharacteristic
173Q8—1884no—
174C2×C4—22no—
175C2×C4—21no—
176C2×C4—22no—
177C2×C4—21no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—474no—
185C2×C4—942no—
186C2×C4—942no—
187C2×C4—942no—
188C2×C4—942no—
189C2×C4—942no—
190C2×C4—942no—
191C2×C4—942no—
192C2×C4—942no—
193C2×C4—942no—
194C2×C4—942no—
195C2×C4—942no—
196C2×C4—1884no—
197C22—22no—
198C22—24no—
199C22—41no—
200C22—42no—
201C22—41no—
202C22C2×Q8×D4711yescharacteristic
203C22#1309406911yescharacteristic
204C22#1309406912yes—
205C22#1309407011yescharacteristic
206C22#1309407112yes—
207C4—41no—
208C4—42no—
209C4—42no—
210C4—41no—
211C4—944no—
212C4—1882no—
213C4—1882no—
214C4—1882no—
215C2—42no—
216C2#1568974811yescharacteristic
217C2#1568975212yes—
218C2#1568986011yescharacteristic
219C2#1568987012yes—
220C2#1568987611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#399C2
hypercenter#399D47
hypocenterC47#2841
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #399

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #15689064C2semidirect
2. #15689056C2semidirect
3. #15689053C2semidirect
5. #15689043C2semidirect
38. C22×Dic47Q8semidirect
120. C47#2841semidirect